2 The sequence of values given by the iterative formula
$$x _ { n + 1 } = \frac { 1 } { 5 } \left( 4 x _ { n } + \frac { 306 } { x _ { n } ^ { 4 } } \right)$$
with initial value \(x _ { 1 } = 3\), converges to \(\alpha\).
- Use this iterative formula to find \(\alpha\) correct to 3 decimal places, showing the result of each iteration.
- State an equation satisfied by \(\alpha\), and hence show that the exact value of \(\alpha\) is \(\sqrt [ 5 ] { 306 }\).